Optimal. Leaf size=28 \[ 4-e^2+\frac {e^{3 x}}{-4+x}+\log \left (-x+\frac {x}{e^4}\right ) \]
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Rubi [A]
time = 0.18, antiderivative size = 17, normalized size of antiderivative = 0.61, number of steps
used = 5, number of rules used = 4, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {1608, 27, 6874,
2228} \begin {gather*} \log (x)-\frac {e^{3 x}}{4-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1608
Rule 2228
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {16-8 x+x^2+e^{3 x} \left (-13 x+3 x^2\right )}{x \left (16-8 x+x^2\right )} \, dx\\ &=\int \frac {16-8 x+x^2+e^{3 x} \left (-13 x+3 x^2\right )}{(-4+x)^2 x} \, dx\\ &=\int \left (\frac {1}{x}+\frac {e^{3 x} (-13+3 x)}{(-4+x)^2}\right ) \, dx\\ &=\log (x)+\int \frac {e^{3 x} (-13+3 x)}{(-4+x)^2} \, dx\\ &=-\frac {e^{3 x}}{4-x}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.23, size = 14, normalized size = 0.50 \begin {gather*} \frac {e^{3 x}}{-4+x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 19, normalized size = 0.68
method | result | size |
norman | \(\frac {{\mathrm e}^{3 x}}{x -4}+\ln \left (x \right )\) | \(14\) |
risch | \(\frac {{\mathrm e}^{3 x}}{x -4}+\ln \left (x \right )\) | \(14\) |
derivativedivides | \(\ln \left (3 x \right )+\frac {3 \,{\mathrm e}^{3 x}}{3 x -12}\) | \(19\) |
default | \(\ln \left (3 x \right )+\frac {3 \,{\mathrm e}^{3 x}}{3 x -12}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 17, normalized size = 0.61 \begin {gather*} \frac {{\left (x - 4\right )} \log \left (x\right ) + e^{\left (3 \, x\right )}}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 10, normalized size = 0.36 \begin {gather*} \log {\left (x \right )} + \frac {e^{3 x}}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 19, normalized size = 0.68 \begin {gather*} \frac {x \log \left (x\right ) + e^{\left (3 \, x\right )} - 4 \, \log \left (x\right )}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 13, normalized size = 0.46 \begin {gather*} \ln \left (x\right )+\frac {{\mathrm {e}}^{3\,x}}{x-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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